若代数式1/2(x+1)+1/6(x+1)+1/12(x+1)+.+1/90(x+1)的值为18,求x的值

题目

若代数式1/2(x+1)+1/6(x+1)+1/12(x+1)+.+1/90(x+1)的值为18,求x的值
在线等哦

答案

1/2(x + 1) + 1/6(x + 1) + 1/12(x + 1)+ ...+1 /90(x + 1) = 18(x + 1) (1/2 + 1/6 + 1/12 + ...+ 1/90) = 18(x + 1) (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/9 - 1/10) = 18(x + 1) (1 - 1/10) = 18(x + 1) (9...